If you're looking to get into anime and you've only seen mainstream stuff like Dragonball Z, Bleach is an ideal place to start. Now I can't say popularity is the best way to measure the quality of something, but the Bleach fanbase is practically a cult following. In my opinion this anime should be on everyone's priority list.
There are too many awesome characters to name, although Zaraki Kenpachi is the king of badassery. For those of you that love long running animes like One Piece and Naruto, Bleach could be your next addiction.
Plot summary taken from IMDB:
High school student Kurosaki Ichigo is unlike any ordinary kid. Why? Because he can see ghosts. Ever since a young age, he's been able to see spirits from the afterlife. Ichigo's life completely changes one day when he and his two sisters are attacked by an evil, hungry and tormented spirit known as a Hollow. Right in the nick of time, Ichigo and his siblings are aided by a Shinigami (Death God) named Kuchiki Rukia, whose responsibility it is to send good spirits (Pluses) to the afterlife known as Soul Society, and to purify Hollows and send them up to Soul Society. But during the fight against the Hollow, Rukia is injured and must transfer her powers to Ichigo. With this newly acquired power, so begins Kurosaki Ichigo's training and duty as a Shinigami to maintain the balance between the world of the living and the world of the dead.
There are a hell of a lot of episodes to watch, as the director Noriyuki Abe and Studio Pierrot has been pumping them out since 2004 and the manga is still ongoing. The mangaka, Tite Kubo uses a simple but fairly unique art style that gives the characters life and personality.
It might take you some time to get into the rhythm of Bleach, possibly up to 100 episodes. But I can assure you it's worth the watch. You'll be humming the intro songs in no time. Some of the characters are unbelievably badass - there's no contest who'd win in a fight versus Ichigo and Naruto. The only bad part is the filler, beware of the Bounto arc.